anonymous 4 years ago how do you solve 16^(-3/4) without a calculator?

1. anonymous

split the powers and then do individually

2. anonymous

what do you mean by split the powers?

3. anonymous

do u got it

4. anonymous

no, im lost where -3 is multiplyed by 6 and then the ^1/4 part

5. anonymous

ok i explain in steps

6. theEric

(-3) means $\frac{1}{16^3}$ and (1/4) means $\sqrt[4]{16}$ right? So, since you're doing both to the 16... it can be written as $\frac{1}{\sqrt[4]{16^3}}$ or $\frac{1}{\sqrt[4]{16}^3}$

7. anonymous

that makes sense so far

8. theEric

Now, one looks much more easy to solve than the other, even though they are the same thing.

9. anonymous

the power is -3/4 base is 16 now 16^-3 . 16^1/4=1/(16)^3.$\sqrt[4]{16}$

10. anonymous

how does $\sqrt[4]{16^3}$ turn into 8?

11. anonymous

i know the answer is 1/8

12. anonymous

$\sqrt[4]{4096}$

13. anonymous

nvm

14. theEric

I would look at it the other way - just to avoid that huge number $16^3$.

15. theEric

$\frac{1}{\sqrt[4]{16}^3}$

16. theEric

So it's like $\frac{1}{(\sqrt[4]{16})^3}$

17. theEric

And what is $\sqrt[4]{16}$?

18. theEric

Guess :P

19. theEric

It's a nice number.

20. anonymous

2

21. anonymous

sorry, i was afk for a while

22. anonymous

then 2^3 is 8

23. anonymous

so 1/8

24. anonymous

thanks!

25. theEric

Understood! Thank you! And you're welcome!